Fuzzy common coarsest partition algorithm

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Given two different partitions of a shape (for argument's sake, two different administrative divisions of a country), how can I find a new partition into which both of those partitions fit, allowing for (and optimising) some error?

For example, ignoring the error, I want an algorithm that does this:



But now imagine that some of these lines are slightly different between the two partitions, so that this perfect answer is not possible, and instead I want the optimal answer subject to minimising some error criterion.



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